1. Technical Field
The present invention relates to a method of annealing, and more particularly, to a method of annealing an optical fiber, an optical waveguide, or a glass tube, having a Bragg grating therein.
2. Description of Related Art
Fiber Bragg gratings have found widespread use in both telecommunications applications and other optical sensor applications. The telecommunications applications may include an optical fiber laser or an optical filter, while the optical sensor applications may include a pressure or temperature sensor in an oil well. Optical devices used in an oil well, which are extremely hazardous environments, are subjected to extremely high temperatures. The operating temperature in a telecommunications environment is substantially less than that for most other sensor applications (80xc2x0 C. vs. typically 200xc2x0 C. in for example an oil well environment). The lower operating temperature impacts the amount of stabilization or heat treatment needed to ensure stable operation. Typically, gratings are heat treated to provide some level of drift stabilization.
For example, U.S. Pat. No. 5,620,496 issued to Erdogan et al., hereinafter the ""496 patent, describes a method for annealing an optical fiber having along some length a radiation induced refractive index difference as in a Bragg grating, i.e. a length along which there is a series of maxima of induced refractive index alternating with a series of minima of induced refractive index. When broadband light is injected into such an optical waveguide and encounters such a grating, some of it will be reflected. The reflected light will have a center wavelength that depends on the spacing between adjacent maxima, and also on the difference between the maximum induced index and the minimum induced index. The induced refractive index difference will decay over time, causing an undesirable drift in the value of the (center) wavelength of the light reflected by the grating. In the method of the ""496 patent, one first monitors, at two temperatures above a desired operating temperature, using two similar optical fibers having a similarly written grating (written by exposure to the interference pattern of two ultraviolet radiation beams), changes over time of the induced refractive index difference, yielding a characteristic decay curve at one of the two temperatures as well as values for the constants of a formula used to extrapolate the decay curve to other temperatures. Next, one extrapolates the characteristic decay curve of the induced refractive index difference, for the operating temperature and for a predetermined annealing temperature (the annealing temperature being higher than the operating temperature so that the induced refractive index difference changes more quickly), and develops mathematically a required annealing time for annealing the optical fiber, the aim of the annealing being to accelerate the changes in the induced refractive index difference to a value that is sufficiently stable for use of the optical fiber in its target environment. More specifically; the induced refractive index difference is changed, by annealing at the annealing temperature, to a value that is such that further changes will be less than a predetermined acceptable amount in a predetermined period of operation at a predetermined operating temperature. In other words, once the optical fiber is annealed for the time determined by the method of the ""496 patent, although the induced refractive index difference will continue to change, it will nevertheless not change significantly over a predetermined operating temperature time (of for example as much as 25 years) at a predetermined operating temperature.
As described in the ""496 patent, an induced refractive index difference in an optical fiber is subject to decay with time and is described for the operating temperature by a characteristic decay curve. The optical fiber is designed to operate at a maximum operating temperature (Top) for a predetermined operating period (xcfx84op), with decay of the induced refractive index difference during the operating period resulting in a change of less than a predetermined amount over the period of operation.
As taught in the ""496 patent, after writing a grating, i.e. inducing a refractive index difference pattern (by for example exposing the optical fiber thorough its cladding to an interference pattern created by the superposition of two coherent ultraviolet light beams), the characteristic decay curve of the induced refractive index difference is then determined for each of two different temperatures, each being greater than the operating temperature (Top). A formula relating the decay curves at different temperatures is then assumed, and the measurements at the two different temperatures are used to determine the constants in the formula. Next, the decay curve at the operating temperature (Top) is extrapolated from one or another of the higher temperature decay curves, using the assumed formula. Then, using the decay curve at the operating temperature, an operating temperature time (top) is determined after which the induced index will change by less than a predetermined acceptable amount. At the operating temperature time so determined, the operating temperature decay curve indicates the value for the induced refractive index difference to which the induced index must be lowered by annealing in order to stabilize the optical fiber. The operating temperature time and the corresponding induced refractive index difference are referred to in the ""496 patent as a point P on the operating temperature decay curve. The grating is then heated at a predetermined anneal temperature (Tan) greater than the operating temperature (Top) for an (accelerated) anneal time (tan), which is less than the operating temperature time (top) in order to achieve a value of decay equivalent to the value represented by the point P on the operating temperature decay curve. The anneal temperature (Tan) and the anneal time (tan) are determined using the equations set forth in the ""496 patent.
The method of the ""496 patent is based on a color center model, described therein. The ""496 patent discloses that the color center model is the basis for the assumed formula for the characteristic decay curve of the induced refractive index difference. More specifically, what is modeled by the assumed formula and what is measured is the difference xcex4n(t) between the maximum and minimum induced index values at a time t, normalized by a quantity xcex4n0 that is the same difference at some reference time (for example, a time shortly after exposure of the optical fiber to ultraviolet radiation to induce, in places, a change in the index). Such a normalized refractive index difference is assumed in the ""496 patent to vary with time, and so yield a characteristic decay curve, according to the formula:                     R        ⁡                  (          t          )                    ≡                        δ          ⁢                      xe2x80x83                    ⁢                      n            ⁡                          (              t              )                                                δ          ⁢                      xe2x80x83                    ⁢                      n            0                                =          1              1        +                  β          ·                      t            α                                ,
where the parameters xcex1 and xcex2 f both depend on temperature, but do not depend on time. The value of xcex1 for the operating temperature Top is designated as xcex1op and so on. Thus, there is a characteristic decay curve at Top and a different characteristic decay curve at other temperatures with the same formula but different values for the parameters.
As mentioned above, the ""496 patent also assumes how the parameters xcex1 and xcex2 vary with temperature, thus allowing a determination at any temperature of the characteristic decay curve of the induced index (or more specifically, the decay curve for the ratio of differences) from the same curve at any other temperature. The ""496 patent assumes that the temperature dependence of xcex1 and xcex2 is given by the set of equations,             β      ⁡              (        T        )              =                  β        0            ⁢              exp        ⁡                  (                      γ            ⁢                          xe2x80x83                        ⁢            T                    )                      ,      xe2x80x83    ⁢            and      ⁢              xe2x80x83            ⁢              α        ⁡                  (          T          )                      =          T              T        0              ,
where xcex20, xcex3, and T0 are constants and are determined by measuring the characteristic decay curves at two temperatures higher than the operating temperature.
The method of the ""496 patent is thus based on two assumptions: the formula for the characteristic decay curve (or, more specifically, the decay curve for the ratio of differences) and the formulae relating the values of the parameters of the characteristic decay curve at any temperature to the values of the parameters at any other temperature. The characteristic decay curve of the induced refractive index difference is never actually measured at the operating temperature. The accuracy of the method of the ""496 patent relies on the accuracy of its two assumptions.
A similar approach is disclosed in U.S. Pat. No. 6,137,931 to Ishikawa et al., hereinafter called the ""931 patent. There the ratio of differences is assumed to be given by the formula,                     R        ⁡                  (          t          )                    ≡                        δ          ⁢                      xe2x80x83                    ⁢                      n            ⁡                          (              t              )                                                δ          ⁢                      xe2x80x83                    ⁢                      n            0                                =                  C        1            ⁢              t                  -                      n            ⁡                          (              T              )                                            ,
the ratio of differences there sometimes referred to as the secular change R(t) of the normalized refractive index difference. Like the ""496 patent, the approach taken in the ""931 patent also assumes formulae for extrapolating the decay curve of the induced refractive index difference from one temperature to another. In the ""931 patent, the extrapolation formulae are, for the parameter C1,
C1≈1, (independent of temperature),
and for the parameter n(T), the so-called law of Arrhenius, i.e.
n(T)=xcexa exp(xe2x88x92xcex3/T),
where the constants xcexa and xcex3 are said to be (approximately) independent of temperature (at least for a range of temperature). Thus, according to the ""931 patent, the decay curve is measured for a range of temperatures and the constants xcexa and xcex3 are determined so that n(T) as given by the law of Arrhenius results in a good fit of the formula R(t)=C1txe2x88x92n(T) to the measured decay curves. The decay curve at the operating temperature (or any other temperature) is then determined by inserting the operating temperature (or any other temperature) into the law of Arrhenius formula to determine n(T) (and by using C1=1). Knowing therefore the decay curves (algebraically, in closed form, with numerical values for all parameters and constants) at the operating temperature and at a predetermined annealing temperature, an anneal time can be determined, as in the ""496 patent, to reduce the induced refractive index difference to a stable value. According to the ""931 patent, using values for xcexa xcex3 of 2.7914 and 1963.2, respectively, and using C1=1, the anneal time tan for reaching the normalized refractive index difference Rstable(t) needed for stability is given by,             t      an        =          exp      ⁢              {                              ln            ⁡                          (                              R                stable                            )                                                          -              κ                        ⁢                          xe2x80x83                        ⁢                          exp              ⁡                              (                                                      -                    γ                                    /                                      T                    an                                                  )                                                    }              ,
where Rstable(t) is determined by examining (as explained in the ""931 patent) the decay curve for the normalized refractive index difference at the operating temperature Top, the decay curve being given by,             R      ⁡              (        t        )              ≡                  δ        ⁢                  xe2x80x83                ⁢                  n          ⁡                      (            t            )                                      δ        ⁢                  xe2x80x83                ⁢                  n          0                      =                    C        1            ⁢              t                  -                      n            ⁡                          (                              T                op                            )                                            =                  t                              -            κ                    ⁢                      xe2x80x83                    ⁢                      exp            ⁡                          (                                                -                  γ                                /                                  T                  op                                            )                                          .      
Both the ""496 patent and the ""931 patent therefore assume one or more equations used to determine by extrapolation the decay curve of the induced refractive index difference at the operating temperature. In the case of the ""931 patent, it is acknowledged that the assumed formulae for the extrapolation are only approximate. In fact, drastically different values for the xcexa and xcex3 parameters are indicated there for different ranges of temperature. The error inherent in such assumptions, although for some applications of no practical consequence, can be unacceptably large for applications where the optical fiber (or other optical device) is expected to remain stable for especially long times.
What is needed, therefore, is a way of determining an anneal time and temperature for an optical fiber, optical waveguide, or other optical device having in places an induced refractive index difference, that does not rely on determining the decay curve for the induced refractive index difference at the operating temperature based on measurements of the decay curve at other (higher) temperatures.
The present invention provides a novel method for determining a heat treatment (annealing) process for stabilizing fiber Bragg gratings (or any other structure created by inducing, in places, a change in the refractive index) in an optical fiber, optical waveguide, a glass tube, or other optical device.
In particular, the present invention provides a method for annealing an optical waveguide having along some lengths an induced refractive index difference that decays over time and so causes drift in the wavelength of reflected light when broadband light is inserted into the optical waveguide. The method uses an assumed decay formula for the induced refractive index difference indicating how the induced refractive index difference decays in time, the assumed decay formula having parameters that depend on temperature. The method includes the steps of: determining the parameters in the assumed decay formula for both an operating temperature and an annealing temperature, the annealing temperature being higher than the operating temperature, by determining values for the parameters so as to fit an observed decay over a measuring time at the operating temperature and at the annealing temperature; and determining an anneal time at the annealing temperature based on a maximum allowed drift at the operating temperature. In operation, an optical waveguide is then annealed at the anneal temperature for the anneal time to provide the necessary heat treatment (annealing) process for stabilizing a Bragg grating.
The technique described below uses actual measured data at the operating temperature (Top) in conjunction with data measured at the anneal temperature (Tan), which is a temperature greater than the operating temperature, to determine a suitable annealing recipe and to predict the stability performance of the grating. The method of the present invention ensures stable operation with respect to wavelength drift (less than 0.1 picometers per week) of the Bragg grating after long exposure to high temperatures (greater than 150xc2x0 C.)
The method may be used to anneal any optical waveguide having a Bragg grating (or having any other structure created by exposing, in places, the structure to an agent for changing the refractive index). For example, the method may be used to anneal the grating in an optical fiber or in a large-diameter waveguide cane or rod structure.
The foregoing and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof, as illustrated in the accompanying drawings.